Optimization of Oligosaccharide Synthesis from Cellobiose by Dextransucrase

There is a growing market for oligosaccharides as sweeteners, prebiotics, anticariogenic compounds, and immunostimulating agents in both food and pharmaceutical industries. Interest in novel carbohydrate-based products has grown because of their reduced toxicity and low immune response. Cellobiose is potentially valuable as a nondigestible sugar. The reaction of cellobiose, as an acceptor with a sucrose as a donor, catalyzed by a dextransucrase from Leuconostoc mesenteroides B-512FMCM, produced a series of cellobio-oligosaccharides. This production system was optimized using a Box–Behnken experimental design for 289 mM of sucrose and 250 mM of cellobiose and 54 U of the enzyme at pH 5.2 and 30 °C, to produce maximum yields of oligosaccharide.     

An upper and lower solution approach for singular boundary value problems with sign changing non‐linearities

We obtain via Schauder's fixed point theorem new results for singular second‐order boundary value problems where our non‐linear term f(t,y,z) is allowed to change sign. In particular, our problem may be singular at y=0, t=0 and/or t=1. Copyright © 2002 John Wiley & Sons, Ltd.     

The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

Stereoselective Peterson Olefinations from Bench‐Stable Reagents and N‐Phenyl Imines

The synthesis of bench‐stable α,α‐bis(trimethylsilyl)toluenes and tris(trimethylsilyl)methane is described and their use in stereoselective Peterson olefinations has been achieved with a wide substrate scope. Product stereoselectivity was poor with carbonyl electrophiles (E/Z ～1:1 to 4:1) though this was significantly improved by employing the corresponding substituted N‐benzylideneaniline (up to 99:1) as an alternative electrophile. The olefination byproduct was identified as N,N‐bis(trimethylsilyl)aniline and could be easily separated from product by aqueous acid extraction. Evidence for an autocatalytic cycle has been obtained.     

Soe fractional integral inequalities involving $$\varvec{}$$-convex functions

In this paper, some fractional integral inequalities involving m-convex functions are established. The presented results are generalizations of the obtained inequalities in Dragomir and Toader (Babe?-Bolyai Math 38:21–28, 1993).     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

The nature of in-plane skeleton Raman modes of P3HT and their correlation to the degree of molecular order in P3HT:PCBM blend thin films

The nature of main in-plane skeleton Raman modes (C=C and C-C stretch) of poly(3-hexylthiophene) (P3HT) in pristine and its blend thin films with [6,6]-phenyl-C(61)-butyric acid methyl ester (PCBM) is studied by resonant and nonresonant Raman spectroscopy and Raman simulations. Under resonant conditions, the ordered phase of P3HT with respect to its disordered phase is identified by (a) a large shift in the C=C mode peak position to lower wavenumber (~21 cm(-1) shift), (b) a narrower fwhm of the C=C mode (~9 cm(-1) narrower), (c) a larger intensity of the C-C mode relative to the C=C mode (~56% larger), and (d) a very small Raman dispersion (~5 cm(-1)) of the C=C mode. The behavior of the C=C and C-C modes of the ordered and disordered phases of P3HT can be explained in terms of different molecular conformations. The C=C mode of P3HT in P3HT:PCBM blend films can be reproduced by simple superposition of the two peaks observed in different phases of P3HT (ordered and disordered). We quantify the molecular order of P3HT after blending with PCBM and the subsequent thermal annealing to be 42 ± 5% and 94 ± 5% in terms of the fraction of ordered P3HT phase, respectively. The increased molecular order of P3HT in blends upon annealing correlates well with enhanced device performance (J(SC), -4.79 to -8.72 mA/cm(2) and PCE, 1.07% to 3.39%). We demonstrate that Raman spectroscopy (particularly under resonant conditions) is a simple and powerful technique to study molecular order of conjugated polymers and their blend films.     

On the Nagumo uniqueness theorem

By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.     

Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.     

Compression-expansion fixed point theorem in two norms and applications

In this paper we present a two-norms version of Krasnoselskii's fixed point theorem in cones. The abstract result is then applied to prove the existence of positive Lp solutions of Hammerstein integral equations with better integrability properties on the kernels.